Quasiperiodic arrangement of magnetodielectric $\delta$-plates: Green's functions and Casimir energies for $N$ bodies

Abstract

We study a variety of finite quasiperiodic configurations with magnetodielectric $\delta$-function plates created from simple substitution rules. While previous studies for $N$ bodies involved interactions mediated by a scalar field, we extended our analysis of Green's function and corresponding Casimir energy to the electromagnetic field using plates with magnetic and dielectric properties for handling finite-size quasiperiodic lattices. The Casimir energy is computed for a class of quasiperiodic structures built from $N$ purely conducting or permeable $\delta$-plates. The Casimir energy of this quasiperiodic sequence of plates turns out to be either positive or negative, indicating that the pressure from the quantum vacuum tends to cause the stack of plates to expand or contract depending on their arrangement. We also handle the transverse electric and transverse magnetic mode Green's functions for $\delta$-plates and derive the Faddeev-like equation with the transition matrix for $N$ purely conducting or permeable plates.

References in corpus (8)

• Casimir forces between arbitrary compact objects
• Casimir energies of self-similar plate configurations
• Casimir-Polder energy for axially symmetric systems
• Repulsive Casimir forces and the role of surface modes
• Switching the sign of the Casimir force between two PEMC spheres
• Casimir repulsion turned into attraction by the nonlocal response of salted water
• Casimir repulsion with biased semiconductors
• Casimir energy of $N$ magnetodielectric $\delta$-function plates

Cited by in corpus (1)

• Casimir energy for $N$ constant conductivity $\delta$-plates with a neural network perception